$ B = \left[\begin{array}{rrr}-1 & -1 & -1 \\ -2 & 2 & -1 \\ 3 & -1 & 1\end{array}\right]$ $ E = \left[\begin{array}{r}4 \\ 0 \\ 0\end{array}\right]$ Is $ B- E$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ E$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ E$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ E$ Do $ B$ and $ E$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ E$ have the same number of columns? No Yes No No Since $ B$ has different dimensions $(3\times3)$ from $ E$ $(3\times1)$, $ B- E$ is not defined.